#pragma region satashun // #pragma GCC optimize("Ofast") // #pragma GCC optimize("unroll-loops") #include using namespace std; using uint = unsigned int; using ll = long long; using ull = unsigned long long; using pii = pair; template using V = vector; template using VV = V>; template V make_vec(size_t a) { return V(a); } template auto make_vec(size_t a, Ts... ts) { return V(ts...))>(a, make_vec(ts...)); } template void fill_vec(T& v, const V& val) { v = val; } template void fill_vec(vector& vec, const V& val) { for (auto& v : vec) fill_vec(v, val); } #define pb push_back #define eb emplace_back #define mp make_pair #define fi first #define se second #define rep(i, n) rep2(i, 0, n) #define rep2(i, m, n) for (int i = m; i < (n); i++) #define per(i, b) per2(i, 0, b) #define per2(i, a, b) for (int i = int(b) - 1; i >= int(a); i--) #define ALL(c) (c).begin(), (c).end() #define SZ(x) ((int)(x).size()) constexpr ll TEN(int n) { return (n == 0) ? 1 : 10 * TEN(n - 1); } template void chmin(T& t, const U& u) { if (t > u) t = u; } template void chmax(T& t, const U& u) { if (t < u) t = u; } template int arglb(const V& v, const T& x) { return distance(v.begin(), lower_bound(ALL(v), x)); } template int argub(const V& v, const T& x) { return distance(v.begin(), upper_bound(ALL(v), x)); } template void mkuni(vector& v) { sort(ALL(v)); v.erase(unique(ALL(v)), end(v)); } template vector sort_by(const vector& v, bool increasing = true) { vector res(v.size()); iota(res.begin(), res.end(), 0); if (increasing) { stable_sort(res.begin(), res.end(), [&](int i, int j) { return v[i] < v[j]; }); } else { stable_sort(res.begin(), res.end(), [&](int i, int j) { return v[i] > v[j]; }); } return res; } // prototype template ostream& operator<<(ostream& os, const pair& p); template ostream& operator<<(ostream& os, const vector& v); template istream& operator>>(istream& is, vector& v); template ostream& operator<<(ostream& os, const array& arr); template ostream& operator<<(ostream& os, const set& ST); template ostream& operator<<(ostream& os, const multiset& ST); template ostream& operator<<(ostream& os, const map& MP); ostream& operator<<(ostream& o, __int128_t x); // io functions template istream& operator>>(istream& is, pair& p) { is >> p.first >> p.second; return is; } template ostream& operator<<(ostream& os, const pair& p) { os << "(" << p.first << "," << p.second << ")"; return os; } template istream& operator>>(istream& is, vector& v) { for (auto& x : v) { is >> x; } return is; } template ostream& operator<<(ostream& os, const vector& v) { os << "{"; rep(i, v.size()) { if (i) os << ","; os << v[i]; } os << "}"; return os; } template ostream& operator<<(ostream& os, const array& arr) { os << '['; for (auto v : arr) os << v << ','; os << ']'; return os; } template ostream& operator<<(ostream& os, const set& ST) { os << "{"; for (auto it = ST.begin(); it != ST.end(); ++it) { if (it != ST.begin()) os << ","; os << *it; } os << "}"; return os; } template ostream& operator<<(ostream& os, const multiset& ST) { os << "{"; for (auto it = ST.begin(); it != ST.end(); ++it) { if (it != ST.begin()) os << ","; os << *it; } os << "}"; return os; } template ostream& operator<<(ostream& os, const map& MP) { for (auto it = MP.begin(); it != MP.end(); ++it) { os << "(" << it->first << ": " << it->second << ")"; } return os; } string to_string(__int128_t x) { if (x == 0) return "0"; string result; if (x < 0) { result += "-"; x *= -1; } string t; while (x) { t.push_back('0' + x % 10); x /= 10; } reverse(t.begin(), t.end()); return result + t; } ostream& operator<<(ostream& o, __int128_t x) { return o << to_string(x); } #ifdef LOCAL void debug_out() { cerr << endl; } template void debug_out(Head H, Tail... T) { cerr << " " << H; debug_out(T...); } #define debug(...) \ cerr << __LINE__ << " [" << #__VA_ARGS__ << "]:", debug_out(__VA_ARGS__) #define dump(x) cerr << __LINE__ << " " << #x << " = " << (x) << endl #else #define debug(...) (void(0)) #define dump(x) (void(0)) #endif template V& operator+=(V& vec, const T& v) { for (auto& x : vec) x += v; return vec; } template V& operator-=(V& vec, const T& v) { for (auto& x : vec) x -= v; return vec; } // suc : 1 = newline, 2 = space template void print(T x, int suc = 1) { cout << x; if (suc == 1) cout << "\n"; else if (suc == 2) cout << " "; } template void print(const vector& v, int suc = 1) { for (int i = 0; i < v.size(); ++i) print(v[i], i == int(v.size()) - 1 ? suc : 2); } template void show(T x) { print(x, 1); } template void show(Head H, Tail... T) { print(H, 2); show(T...); } int topbit(int t) { return t == 0 ? -1 : 31 - __builtin_clz(t); } int topbit(ll t) { return t == 0 ? -1 : 63 - __builtin_clzll(t); } int botbit(int a) { return a == 0 ? 32 : __builtin_ctz(a); } int botbit(ll a) { return a == 0 ? 64 : __builtin_ctzll(a); } int popcount(int t) { return __builtin_popcount(t); } int popcount(ll t) { return __builtin_popcountll(t); } int bit_parity(int t) { return __builtin_parity(t); } int bit_parity(ll t) { return __builtin_parityll(t); } struct prepare_io { prepare_io() { cin.tie(nullptr); ios::sync_with_stdio(false); cout << fixed << setprecision(10); } } prep_io; #pragma endregion satashun // init_dag : yuki 1678, ABC214H template // capacity, distance struct MinCostFlow { struct edge { int to, rev; C cap; D cost; edge(int to, C cap, D cost, int rev) : to(to), cap(cap), cost(cost), rev(rev){}; }; using E = edge; const D INF = numeric_limits::max() / D(3); int n; VV g; V h, dst; V prevv, preve; MinCostFlow(int n) : n(n), g(n), h(n), dst(n), prevv(n), preve(n) {} void add_edge(int f, int t, C cap, D cost) { g[f].emplace_back(t, cap, cost, (int)g[t].size()); g[t].emplace_back(f, 0, -cost, (int)g[f].size() - 1); } void init_dag(int s) { fill(h.begin(), h.end(), INF); h[s] = 0; V vis(n); // topological sort V vs; auto topo = [&](auto&& f, int v) -> void { vis[v] = 1; for (auto& e : g[v]) { if (e.cap > 0 && !vis[e.to]) { f(f, e.to); } } vs.pb(v); }; for (int i = 0; i < n; ++i) { if (!vis[i]) topo(topo, i); } reverse(vs.begin(), vs.end()); for (int v : vs) { if (h[v] == INF) continue; for (auto& e : g[v]) { if (e.cap > 0) { chmin(h[e.to], h[v] + e.cost); } } } } // true : no negative cycle bool init_negative(int s) { fill(h.begin(), h.end(), INF); h[s] = 0; for (int t = 0; t <= n; ++t) { for (int i = 0; i < n; ++i) { for (auto e : g[i]) { if (!e.cap) continue; if (h[e.to] > h[i] + e.cost && t == n) { return false; } h[e.to] = min(h[e.to], h[i] + e.cost); } } } return true; } D exec(int s, int t, C f, bool full = false) { if (full) f = INF; D res = 0; using Data = pair; while (f > 0) { priority_queue, greater> que; fill(dst.begin(), dst.end(), INF); dst[s] = 0; que.push(Data(0, s)); while (!que.empty()) { auto p = que.top(); que.pop(); int v = p.second; if (dst[v] < p.first) continue; rep(i, g[v].size()) { auto e = g[v][i]; D nd = dst[v] + e.cost + h[v] - h[e.to]; if (e.cap > 0 && dst[e.to] > nd) { dst[e.to] = nd; prevv[e.to] = v; preve[e.to] = i; que.push(Data(dst[e.to], e.to)); } } } if (dst[t] == INF) { if (full) { return res; } else { return D(-INF); } } rep(i, n) if (dst[i] != INF) h[i] += dst[i]; C d = f; for (int v = t; v != s; v = prevv[v]) { d = min(d, g[prevv[v]][preve[v]].cap); } f -= d; res += d * h[t]; for (int v = t; v != s; v = prevv[v]) { edge& e = g[prevv[v]][preve[v]]; e.cap -= d; g[v][e.rev].cap += d; } } return res; } }; void slv() { // input int N, M; cin >> N >> M; MinCostFlow g(N); rep(i, M) { int u, v, c, d; cin >> u >> v >> c >> d; --u, --v; g.add_edge(u, v, 1, c); g.add_edge(u, v, 1, d); g.add_edge(v, u, 1, c); g.add_edge(v, u, 1, d); } // solve ll ans = g.exec(0, N - 1, 2); show(ans); } int main() { int cases = 1; // cin >> cases; rep(i, cases) slv(); return 0; }